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On finite dimensional realizations for the term structure of futures prices
Stockholm School of Economics.
Stockholm School of Economics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2006 (English)In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 9, no 3, 281-314 p.Article in journal (Refereed) Published
Abstract [en]

    We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including a recently developed model for gas futures. In particular we provide necessary and sufficient conditions for when the induced spot price is a Markov process. In particular we can prove that the only HJM type futures price models with spot price dependent volatility structures which genetically possess a spot price realization are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.

Place, publisher, year, edition, pages
2006. Vol. 9, no 3, 281-314 p.
Keyword [en]
HJM models, factor models, state space models, Markovian realizations
National Category
Economics and Business Mathematics
URN: urn:nbn:se:kth:diva-86552DOI: 10.1142/S0219024906003639ScopusID: 2-s2.0-33646747696OAI: diva2:500831
QC 20120313Available from: 2012-02-13 Created: 2012-02-13 Last updated: 2012-03-13Bibliographically approved

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Björk, TomasLandén, Camilla
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